Question

once a year, a store offers a free frozen yogurt to its customers. each customer can choose one flavor of frozen yogurt and one topping. there are 8 possible ways to order the frozen yogurt. how many flavors and toppings could the customers choose from? 2 flavors and 4 toppings 2 flavors and 2 toppings 4 flavors and 3 toppings 4 flavors and 4 toppings

Explanation:

Step1: Recall the multiplication principle

The number of ways to choose one flavor and one topping is the product of the number of flavors and the number of toppings. Let \( f \) be the number of flavors and \( t \) be the number of toppings, so the total number of ways is \( f\times t \).

Step2: Check each option

• For "2 flavors and 4 toppings": \( 2\times4 = 8 \), which matches the total number of ways (8).
• For "2 flavors and 2 toppings": \( 2\times2 = 4

eq8 \).

• For "4 flavors and 3 toppings": \( 4\times3 = 12

eq8 \).

• For "4 flavors and 4 toppings": \( 4\times4 = 16

eq8 \).

Answer:

2 flavors and 4 toppings